It's clear that Peter intends to break the promise. What I don't get however is why people are so up in arms about that.

Peter is a teenager and no teenager is flawless. Also, they are so much in love, you can't blame him.

Yes, the way he says "Yeah but those are the best kind" is definitely unnecessarily cold and her smiling feels a little weird considering her dad had recently died and Peter refers to his last words in that kind of way. I can definitely see why people have a problem with that aspect alone.

However, the general idea of him breaking the promise really shouldn't be a problem if you ask me. A dying wish from someone who doesn't even seem to understand how much they like each other shouldn't be of more importance than their love life.

Sure, it's a huge risk but they both know that. It would've been another thing if Gwen didn't know he was Spider-Man. But they both know and they both still want to be together. And Peter will suffer because of this and that will make him realise that him being Spider-Man will put others at risk as well. It's there for the sake of the story.